A fourth-order combined compact upwind (CCU) finite difference scheme with high resolving efficiency is proposed. A high-order compact difference algorithm for Navier-Stokes (NS) equations based on projection method is developed with CCU scheme on staggered grids. Convection terms are discretized by CCU scheme. Viscous terms, pressure gradient terms and pressure Poisson equations are discretized with fourth-order compact symmetric finite difference schemes. Numerical examples validate capability of the proposed approach. It is shown that the method is accurate and robust, and is applicable to complex fluid flows.

On the steady convection-diffusion equation,a new method is developed for construction of high-order compact finitedifference scheme.First,the two-dimensional equation are transformed into the two equations,which are similar to the form of onedimensional equation,and are subsequently discretized by utilizing compact difference formula proposed for the one-dimensional equation in[6].Then,a compact difference scheme that is O(h⁴+h²k²+k⁴) on the nine-point 2-D stencil for the steady convectiondiffusion equation is established.Finally,numerical example is given to illustrate the present method.